1. …new vocabulary from Hawking Chaps 9-11 Arrow of time time: an imaginery dimension; spacelike & timelike conjugate variables 4 space-time vectors: e.g. (x, y, z, ict), (p x,p y,p z,iE/c) CPT maximal P and C violation: Madam Wu looking at radioactive decay CP good to high level of accuracy…but fails at amplitude 10 -3 T, microscopic time reversal CP violation leads to matter asymmetry in early universe …and proton decay today, though not yet observed Entropy…increase of disorder in an isolated system, more phase space in a disordered system than in an ordered one 2 nd Law of Thermodynamics…entropy increases (unless you do work)

2. Kurt Gödel’s incompleteness theorem: impossible to prove all true statements valid for arithmetic…and by extension all theories based on math Feynman graphs: forward particle in time = backward going antiparticle Casimir force between 2 metal plates: macro proof of virtual particles existence of negative energy in vacuum between plates  by extension, positive vacuum energy outside plates

3. …new vocabulary…chapters 11&12 of “Time” GR + QM: no singularities in quantum world  extended objects may exist? “strings”? GUT = Grand Unified Theories: EM + Weak + Strong unification scale = 10 15 GeV Planck: time…mass = energy = temperature = 10 19 GeV Relativistic γ factor quantifies life near c Lorentz contraction: observed objects shortened along path time dilation: observed clocks run slower, time intervals longer

4. Relativistic γ factor: Lorentz contraction, time dilation natural unit of velocity, dimensionless β = v/c natural unit of relativity, dimensionless γ = 1/√(1-(v/c)) 2 watch her go c fast? a) she’s squashed, in direction of motion, and b) her watch time slowed